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# How many...

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666
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How many positive integers are there whose digits strictly increase from left to right?
(For example, 28, 13589, and  4 are all such integers. "Strictly" means no two digits can be equal, so 15668 wouldn't count.)

Jul 13, 2018

#1
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But what is the upper limit? up to 10,000, 100,000, 1,000,000......etc.

Jul 13, 2018
#2
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Since no repeating digits 9 digits available

Guest Jul 14, 2018
#3
+1

How many positive integers are there whose digits strictly increase from left to right?
(For example, 28, 13589, and  4 are all such integers. "Strictly" means no two digits can be equal, so 15668 wouldn't count.)

e.g.

How many ways can 5 digits can be chosen from 9

9C5 = 126

Each of these will have only 1 number in the order needed.

So that is 126 in 5 digit numbers

Do 1 digit numbers and/or 0 count?

there are 10 of those.

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1 digit numbers 10  (includes 0)

2 digit numbers  9C2 = 36

3 digit numbers  9C3 =84

4 digit numbers 9C4=126

5 digit number 9C5 = 126

6 digit numbers 9C6=84

7 digit numbers 9C7=36

8 digit numbers 9C8=9

9 digit numbers = 1

10+36+84+126+126+84+36+9+1 = 512 ways

Jul 14, 2018